Golf ball dimple profile

CROSS-REFERENCE TO RELATED APPLICATIONS

0001This application is a continuation-in-part of co-pending U.S. patent application Ser. No. 14/985,476, filed Dec. 31, 2015, and a continuation-in-part of co-pending U.S. patent application Ser. No. 14/985,482, filed Dec. 31, 2015, and a continuation-in-part of co-pending U.S. patent application Ser. No. 14/985,617, filed Dec. 31, 2015, which are continuations-in-part of U.S. patent application Ser. No. 14/953,641, filed Nov. 30, 2015, which is a continuation-in-part of U.S. patent application Ser. No. 14/835,819, filed Aug. 26, 2015, now abandoned, which is a continuation of U.S. patent application Ser. No. 13/341,652 filed Dec. 30, 2011, now abandoned, the entire disclosures of which are hereby incorporated by reference.

FIELD OF THE INVENTION

0002The present invention is directed to a golf ball dimple cross-sectional profile defined by the product of a base profile and one or more weighting functions.

BACKGROUND OF THE INVENTION

0003U.S. Pat. No. 4,681,323 to Alaki et al. discloses a golf ball with a plurality of recessed dimples having a shape in accordance with a certain mathematical ratio on the surface thereof.

0004U.S. Pat. No. 4,840,381 to Ihara et al. discloses a golf ball characterized by the shape of its dimples. The dimples have a more gentle transition over their edge portion than prior art golf balls wherein dimple edges sharply intrude into the ball surface.

0005U.S. Pat. No. 6,331,150 to Ogg discloses a golf ball having a surface thereon with a plurality of dimples on the surface. The contour of each of the dimples is continuous from a first edge of each of the dimples to a second opposing edge of each of the dimples.

0006Additional background references include, for example, U.S. Pat. No. 4,813,677 to Oka et al. and U.S. Pat. No. 4,840,381 to Ihara et al.

SUMMARY OF THE INVENTION

0007According to one embodiment of the present invention, a golf ball is provided comprising a plurality of recessed dimples on the surface thereof, where at least one dimple has a cross-sectional profile defined by a weighted function, and where the weighted function is the multiplication of a spherical base profile function g(x) and at least one weighting function w(x) and at least a second dimple has a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a conical base profile function g(x) and at least one weighting function w(x).

0008At least one additional dimple may have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x). At least one dimple of the golf ball may have a base dimple profile modified using a pure weighting method, where f(x)=g(x)*(w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. At least one dimple of the golf ball may have a base dimple profile modified using a profile relative method, where f(x)=g(x)*(1+w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. Moreover, a golf ball may be provided where each dimple cross-section is defined by weighting functions. The number of dimples using the first weighted base profile may be equal to the number of dimples using the second weighted base profile. Alternatively, the number of dimples using the first weighted base profile and the number of dimples using the second weighted base profile are not equal to each other. Furthermore, the golf ball may have one or more dimples having cross-sections not defined by a weighting function.

0009According to another embodiment of the present invention, a golf ball is provided comprising a plurality of recessed dimples on the surface thereof, where at least one dimple has a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a spherical base profile function g(x) and at least one weighting function w(x) and at least a second dimple has a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x).

0010At least one dimple of the golf ball may have a base dimple profile modified using a pure weighting method, where f(x)=g(x)*(w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. At least one dimple of the golf ball may have a base dimple profile modified using a profile relative method, where f(x)=g(x)*(1+w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. Moreover, a golf ball may be provided where each dimple cross-section of the golf ball may be defined by a weighting function. The number of dimples using the first weighted base profile may be equal to the number of dimples using the second weighted base profile. Alternatively, the number of dimples using the first weighted base profile may not be equal to the number of dimples using the second weighted base profile. Furthermore, the golf ball may have one or more dimples with cross-sections not defined by a weighting function.

0011According yet to another embodiment, a golf ball may be provided having a plurality of recessed dimples on the surface thereof, where at least one dimple has a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x) and at least a second dimple has a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a conical base profile function g(x) and at least one weighting function w(x).

0012At least one dimple of the golf ball may have a base dimple profile modified using a pure weighting method, where f(x)=g(x)*(w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. At least one dimple of the golf ball may have a base dimple profile modified using a profile relative method, where f(x)=g(x)*(1+w(x)) and where the weighting function w(x) is continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter, and g(x) and f(x) are equal at x=d/2. Moreover, a golf ball may be provided where each dimple cross-section may be defined by a weighting function. The number of dimples using the first weighted base profile may be equal to the number of dimples using the second weighted base profile. Alternatively, the number of dimples using the first weighted base profile may not be equal to the number of dimples using the second weighted base profile. Furthermore, one or more dimples may have cross-sections not defined by a weighting function.

0013The present invention is generally directed to a golf ball having a plurality of recessed dimples on the surface thereof, at least a portion of which have a cross-sectional profile defined by a weighted profile. The weighted profile is the product of a base profile and at least one weighting function. In a particular embodiment, the base profile is defined by a single function. In another particular embodiment, the base profile is defined by a single continuous, differentiable function.

BRIEF DESCRIPTION OF DRAWINGS

0014In the accompanying drawings, which form a part of the specification and are to be read in conjunction therewith, and which are given by way of illustration only, and thus are not meant to limit the present invention:

0015<figref idref="DRAWINGS">FIG. 1</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to one embodiment of the present invention.

0016<figref idref="DRAWINGS">FIG. 2</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0017<figref idref="DRAWINGS">FIG. 3</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0018<figref idref="DRAWINGS">FIG. 4</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0019<figref idref="DRAWINGS">FIG. 5</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0020<figref idref="DRAWINGS">FIG. 6</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0021<figref idref="DRAWINGS">FIG. 7</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0022<figref idref="DRAWINGS">FIG. 8</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0023<figref idref="DRAWINGS">FIG. 9</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0024<figref idref="DRAWINGS">FIG. 10</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0025<figref idref="DRAWINGS">FIG. 11</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0026<figref idref="DRAWINGS">FIG. 12</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0027<figref idref="DRAWINGS">FIG. 13</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0028<figref idref="DRAWINGS">FIG. 14</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0029<figref idref="DRAWINGS">FIG. 15</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0030<figref idref="DRAWINGS">FIG. 16</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0031<figref idref="DRAWINGS">FIG. 17</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0032<figref idref="DRAWINGS">FIG. 18</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0033<figref idref="DRAWINGS">FIG. 19</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0034<figref idref="DRAWINGS">FIG. 20</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0035<figref idref="DRAWINGS">FIG. 21</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0036<figref idref="DRAWINGS">FIG. 22</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0037<figref idref="DRAWINGS">FIG. 23</figref> shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

0038<figref idref="DRAWINGS">FIG. 24</figref> is a partial sectional view of a dimple of a finished ball including layers of paint and a clear coat.

0039<figref idref="DRAWINGS">FIGS. 25<i>a</i>-25<i>d </i></figref>are isometric views of a dimple depicting the enclosed chord volume between the dimple surface and chord plane.

0040<figref idref="DRAWINGS">FIG. 26</figref> shows the preferred and most preferred plan shape area and surface volume ranges according to the present invention.

0041<figref idref="DRAWINGS">FIG. 27</figref> shows a dimple cross-sectional profile of the spherical base dimple profile.

0042<figref idref="DRAWINGS">FIGS. 28<i>a</i>-28<i>c </i></figref>shows the weighting function w(x)=x, the full weighted profile f(x) using profile relative weighting and the full weighted profile f(x) using pure weighting.

0043<figref idref="DRAWINGS">FIGS. 29<i>a</i>-29<i>c </i></figref>shows the weighting function w(x)=−x⁴+x³+2x, the full weighted profile f(x) using profile relative weighting, and the full weighted profile f(x) using pure weighting.

0044<figref idref="DRAWINGS">FIG. 30</figref> shows a dimple cross-sectional profile of the catenary base dimple profile.

0045<figref idref="DRAWINGS">FIGS. 31<i>a</i>-31<i>c </i></figref>shows the weighting function w(x)=x, the full weighted profile f(x) using profile relative weighting and the full weighted profile f(x) using pure weighting.

0046<figref idref="DRAWINGS">FIGS. 32<i>a</i>-32<i>c </i></figref>shows the weighting function w(x)=−x⁴+x³+2x, the full weighted profile f(x) using profile relative weighting, and the full weighted profile f(x) using pure weighting.

0047<figref idref="DRAWINGS">FIG. 33</figref> shows a dimple cross-sectional profile of the conical base dimple profile.

0048<figref idref="DRAWINGS">FIGS. 34<i>a</i>-34<i>c </i></figref>shows the weighting function w(x)=x, the full weighted profile f(x) using profile relative weighting and the full weighted profile f(x) using pure weighting.

0049<figref idref="DRAWINGS">FIGS. 35<i>a</i>-35<i>c </i></figref>shows the weighting function w(x)=−x⁴+x³+2x, the full weighted profile f(x) using profile relative weighting, and the full weighted profile f(x) using pure weighting.

0050<figref idref="DRAWINGS">FIG. 36</figref> illustrates 1/12 of a golf ball according to an embodiment of the present invention.

0051<figref idref="DRAWINGS">FIG. 37</figref> illustrates 1/12 of a golf ball according to an embodiment of the present invention.

0052<figref idref="DRAWINGS">FIG. 38</figref> illustrates 1/12 of a golf ball according to an embodiment of the present invention.

DETAILED DESCRIPTION

0053Golf balls of the present invention include dimples having a cross-sectional shape defined by a weighted profile, the weighted profile being the product of a base dimple profile and at least one weighting function. Suitable base dimple profiles include those that can be defined by a single function, including, but not limited to, spherical, conical, catenary, elliptical, polynomial, Witch of Agnesi, frequency, Neiles parabola, and cosine profiles, and those that are defined by two or more functions, including, but not limited to, profiles comprising a top conical edge and a bottom spherical cap. Profiles comprising a top conical edge and a bottom spherical cap are further disclosed, for example, in U.S. Patent Application Publication No. 2010/0240474, the entire disclosure of which is hereby incorporated herein by reference. In a particular embodiment, the base dimple profile is defined by a single continuous, differentiable function.

0054One or more continuous weighting functions are applied as multiplicative constructs to the base dimple profile to produce the weighted dimple profile. For base profiles defined by a single function the weighting function(s) are applied to the entire dimple profile. For base profiles defined by two or more functions, the weighting function(s) are applied independently to one or more of the base profile functions.

0055Typical weighting function forms include, but are not limited to, polynomial, exponential, and trigonometric, Gaussian or linear combinations thereof.

0056In a particular embodiment, one or more continuous weighting functions are applied as multiplicative constructs to a base dimple profile defined by a single continuous, differentiable function, resulting in a continuous, differentiable weighted dimple profile. It will be appreciated that the weighting function allows dimple profile refinement through biasing derivatives of the function profile, thus allowing specific regions of the dimple cross-section to be altered. This allows unique dimple profiles to be created and provides greater control and flexibility of the final golf ball surface. Furthermore, the method is well suited to common hob manufacturing methods.

0057Non-limiting examples of particularly suitable weighting functions are shown in Table 1 below.

0058<tables id="TABLE-US-00001" num="00001"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="2"><colspec colname="1" colwidth="112pt" align="center" /><colspec colname="2" colwidth="105pt" align="left" /><thead><row><entry namest="1" nameend="2" rowsep="1">TABLE 1</entry></row><row><entry namest="1" nameend="2" align="center" rowsep="1" /></row><row><entry>Example </entry><entry>Weighting </entry></row><row><entry>No.</entry><entry>Function</entry></row><row><entry namest="1" nameend="2" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="2"><colspec colname="1" colwidth="112pt" align="char" char="." /><colspec colname="2" colwidth="105pt" align="left" /><tbody valign="top"><row><entry>1</entry><entry>w = 1</entry></row><row><entry>2</entry><entry>w = x</entry></row><row><entry>3</entry><entry>w = x²</entry></row><row><entry>4</entry><entry>w = x³</entry></row><row><entry>5</entry><entry>w = x⁴</entry></row><row><entry>6</entry><entry>w = x⁴+ x³</entry></row><row><entry>7</entry><entry>w = x²/5 + 3x³+ x⁴</entry></row><row><entry>8</entry><entry>w = 10x²+ 3x⁴</entry></row><row><entry>9</entry><entry>w = 3x⁴+ x³/2 + 10x</entry></row><row><entry>10</entry><entry>w = −x</entry></row><row><entry>11</entry><entry>w = −x³</entry></row><row><entry>12</entry><entry>w = x³− X⁴− 2x</entry></row><row><entry>13</entry><entry>w = sin(x)</entry></row><row><entry>14</entry><entry>w = cos(x)</entry></row><row><entry>15</entry><entry>w = −x⁵</entry></row><row><entry>16</entry><entry>w = e^x</entry></row><row><entry>17</entry><entry>w = −e^x</entry></row><row><entry>18</entry><entry>w = (−e^2x)sin(x)</entry></row><row><entry>19</entry><entry>w = e^2xx³</entry></row><row><entry>20</entry><entry>w = cos(4.9x)/−5</entry></row><row><entry>21</entry><entry>w = cos(1.89x)/−2</entry></row><row><entry>22</entry><entry>w = sin(3.64x)/1.5</entry></row><row><entry>23</entry><entry>w = sin(6x)/3</entry></row><row><entry namest="1" nameend="2" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0059<figref idref="DRAWINGS">FIGS. 1-23</figref> show the final weighted profile defined by the product of a spherical base profile and each of weighting functions 1-23 in Table 1, respectively, with a base profile such that the golf ball diameter is 1.680 inches, the dimple diameter is 0.200 inches, and the base profile has a dimple edge angle of 14°, a chord depth of 0.0063 inches, a surface depth of 0.0122 inches, a dimple radius of 0.7953 inches, and a cap height of 0.0059 inches. The chord depth, equivalent spherical edge angle, edge angle, and weighted volume ratio of the final weighted profile illustrated in each of <figref idref="DRAWINGS">FIGS. 1-23</figref> is given in Table 2 below.

0060<tables id="TABLE-US-00002" num="00002"><table frame="none" colsep="0" rowsep="0" pgwide="1"><tgroup align="left" colsep="0" rowsep="0" cols="2"><colspec colname="offset" colwidth="140pt" align="left" /><colspec colname="1" colwidth="133pt" align="center" /><thead><row><entry /><entry namest="offset" nameend="1" rowsep="1">TABLE 2</entry></row></thead><tbody valign="top"><row><entry /><entry namest="offset" nameend="1" align="center" rowsep="1" /></row><row><entry /><entry>Final Weighted Profile</entry></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="7"><colspec colname="1" colwidth="28pt" align="center" /><colspec colname="2" colwidth="42pt" align="left" /><colspec colname="3" colwidth="70pt" align="left" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="35pt" align="center" /><colspec colname="6" colwidth="35pt" align="center" /><colspec colname="7" colwidth="35pt" align="center" /><tbody valign="top"><row><entry /><entry /><entry /><entry /><entry>equivalent</entry><entry /><entry /></row><row><entry /><entry /><entry /><entry>chord</entry><entry>spherical</entry><entry>edge</entry><entry>weighted</entry></row><row><entry /><entry /><entry /><entry>depth</entry><entry>edge angle</entry><entry>angle</entry><entry>volume</entry></row><row><entry>FIG. #</entry><entry>Base Profile</entry><entry>Weighting Function</entry><entry>(inches)</entry><entry>(degrees)</entry><entry>(degrees)</entry><entry>ratio</entry></row><row><entry namest="1" nameend="7" align="center" rowsep="1" /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="7"><colspec colname="1" colwidth="28pt" align="char" char="." /><colspec colname="2" colwidth="42pt" align="left" /><colspec colname="3" colwidth="70pt" align="left" /><colspec colname="4" colwidth="28pt" align="char" char="." /><colspec colname="5" colwidth="35pt" align="char" char="." /><colspec colname="6" colwidth="35pt" align="char" char="." /><colspec colname="7" colwidth="35pt" align="char" char="." /><tbody valign="top"><row><entry>1</entry><entry>spherical</entry><entry>w = 1</entry><entry>0.0126</entry><entry>21.08°</entry><entry>20.95°</entry><entry>2.00</entry></row><row><entry>2</entry><entry>spherical</entry><entry>w = x</entry><entry>0.0063</entry><entry>17.75°</entry><entry>20.94°</entry><entry>1.53</entry></row><row><entry>3</entry><entry>spherical</entry><entry>w = x²</entry><entry>0.0063</entry><entry>16.32°</entry><entry>20.93°</entry><entry>1.33</entry></row><row><entry>4</entry><entry>spherical</entry><entry>w = x³</entry><entry>0.0063</entry><entry>15.57°</entry><entry>20.92°</entry><entry>1.23</entry></row><row><entry>5</entry><entry>spherical</entry><entry>w = x⁴</entry><entry>0.0063</entry><entry>15.13°</entry><entry>20.90°</entry><entry>1.17</entry></row><row><entry>6</entry><entry>spherical</entry><entry>w = x⁴+ x³</entry><entry>0.0063</entry><entry>15.35°</entry><entry>20.91°</entry><entry>1.20</entry></row><row><entry>7</entry><entry>spherical</entry><entry>w = x²/5 + 3x³+ x⁴</entry><entry>0.0063</entry><entry>15.50°</entry><entry>20.92°</entry><entry>1.22</entry></row><row><entry>8</entry><entry>spherical</entry><entry>w = 10x²+ 3x⁴</entry><entry>0.0063</entry><entry>16.05°</entry><entry>20.93°</entry><entry>1.29</entry></row><row><entry>9</entry><entry>spherical</entry><entry>w = 3x⁴+ x³/2 + 10x</entry><entry>0.0063</entry><entry>15.73°</entry><entry>20.91°</entry><entry>1.25</entry></row><row><entry>10</entry><entry>spherical</entry><entry>w = −x</entry><entry>0.0126</entry><entry>17.27°</entry><entry>14.00°</entry><entry>1.47</entry></row><row><entry>11</entry><entry>spherical</entry><entry>w = −x³</entry><entry>0.0126</entry><entry>19.45°</entry><entry>14.02°</entry><entry>1.77</entry></row><row><entry>12</entry><entry>spherical</entry><entry>w = x³− x⁴− 2x</entry><entry>0.0126</entry><entry>17.49°</entry><entry>14.01°</entry><entry>1.50</entry></row><row><entry>13</entry><entry>spherical</entry><entry>w = sin(x)</entry><entry>0.0063</entry><entry>18.93°</entry><entry>20.95°</entry><entry>1.70</entry></row><row><entry>14</entry><entry>spherical</entry><entry>w = cos(x)</entry><entry>0.0126</entry><entry>18.43°</entry><entry>14.00°</entry><entry>1.63</entry></row><row><entry>15</entry><entry>spherical</entry><entry>w = −x⁵</entry><entry>0.0063</entry><entry>15.42°</entry><entry>14.05°</entry><entry>1.21</entry></row><row><entry>16</entry><entry>spherical</entry><entry>w = e^x</entry><entry>0.0063</entry><entry>17.04°</entry><entry>20.94°</entry><entry>1.43</entry></row><row><entry>17</entry><entry>spherical</entry><entry>w = −e^x</entry><entry>0.0126</entry><entry>17.98°</entry><entry>14.01°</entry><entry>1.57</entry></row><row><entry>18</entry><entry>spherical</entry><entry>w = (−e^2x)sin(x)</entry><entry>0.0063</entry><entry>14.98°</entry><entry>14.02°</entry><entry>1.15</entry></row><row><entry>19</entry><entry>spherical</entry><entry>w = e^2xx³</entry><entry>0.0063</entry><entry>15.02°</entry><entry>13.98°</entry><entry>1.15</entry></row><row><entry>20</entry><entry>Spherical</entry><entry>w = cos(4.9x)/−5</entry><entry>0.0050</entry><entry>14.00°</entry><entry>13.76°</entry><entry>1.00</entry></row><row><entry>21</entry><entry>Spherical</entry><entry>w = cos(1.89x)/−2</entry><entry>0.0031</entry><entry>14.00°</entry><entry>17.47°</entry><entry>1.00</entry></row><row><entry>22</entry><entry>Spherical</entry><entry>w = sin(3.64x)/1.5</entry><entry>0.0063</entry><entry>14.00°</entry><entry>11.41°</entry><entry>1.00</entry></row><row><entry>23</entry><entry>Spherical</entry><entry>w = sin(6x)/3</entry><entry>0.0063</entry><entry>14.00°</entry><entry>14.02°</entry><entry>1.00</entry></row><row><entry namest="1" nameend="7" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0061For purposes of the present disclosure, a spherical base profile is defined by the following function:

0062<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mrow><mrow><mo>-</mo><msqrt><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mrow><mo>+</mo><msqrt><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mi>d</mi><mn>2</mn></mfrac><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mrow></mrow></math></maths><br /> Where, for the above formula, the origin is located along the dimple axis intersecting the chord plane at y=0, and wherein

0063<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mrow><mrow><mi>R</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mrow><mn>2</mn><mo>⁢</mo><mrow><mi>cos</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mi>θ</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>π</mi></mrow><mn>180</mn></mfrac><mo>+</mo><mrow><mi>acos</mi><mo>⁡</mo><mrow><mo>(</mo><mfrac><mi>d</mi><mi>D</mi></mfrac><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mfrac></mrow><mo>;</mo></mrow></math></maths><br /> θ=the dimple edge angle, in degrees; <br /> d=the dimple diameter, in inches; and <br /> D=the diameter of the golf ball, in inches.

0064<tables id="TABLE-US-00003" num="00003"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="5"><colspec colname="offset" colwidth="21pt" align="left" /><colspec colname="1" colwidth="63pt" align="left" /><colspec colname="2" colwidth="56pt" align="center" /><colspec colname="3" colwidth="28pt" align="center" /><colspec colname="4" colwidth="49pt" align="center" /><thead><row><entry /><entry namest="offset" nameend="4" rowsep="1">TABLE 3</entry></row><row><entry /><entry namest="offset" nameend="4" align="center" rowsep="1" /></row><row><entry /><entry /><entry>Edge </entry><entry /><entry>Chord </entry></row><row><entry /><entry>Figures</entry><entry>Angle</entry><entry>Volume</entry><entry>Depth</entry></row><row><entry /><entry namest="offset" nameend="4" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /><entry>FIG. 1</entry><entry>D</entry><entry>D</entry><entry>D</entry></row><row><entry /><entry>FIGS. 2-9, 13, 16</entry><entry>D</entry><entry>D</entry><entry>S</entry></row><row><entry /><entry>FIGS. 10-12, 14, 17</entry><entry>S</entry><entry>D</entry><entry>D</entry></row><row><entry /><entry>FIGS. 15, 18, 19</entry><entry>S</entry><entry>D</entry><entry>S</entry></row><row><entry /><entry>FIG. 20</entry><entry>S</entry><entry>S</entry><entry>D</entry></row><row><entry /><entry>FIG. 21</entry><entry>D</entry><entry>S</entry><entry>D</entry></row><row><entry /><entry>FIG. 22</entry><entry>D</entry><entry>S</entry><entry>S</entry></row><row><entry /><entry>FIG. 23</entry><entry>S</entry><entry>S</entry><entry>S</entry></row><row><entry /><entry namest="offset" nameend="4" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0065In Table 3, S signifies that the property for the base dimple profile and the weighted dimple profile are the same and D signifies that the property for the base dimple profile and the weighted dimple profile are different. Due to the nature of manufacture, differences in edge angle of less than about 0.25 degrees are considered substantially the same. Similarly, dimensional differences in dimple chord depth of about 0.0003 inches or less would constitute substantially the same chordal depth. Lastly, differences in chordal volume of about 3.5×10⁻⁶inches squared or less would constitute substantially the same chordal volume.

0066A golf ball according to the present invention has a plurality of recessed dimples on the surface thereof, where the dimples have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a single continuous, differentiable function and at least one weighting function. The weighting function is selected from the group consisting of polynomial, exponential and trigonometric functions. Examples of these functions are listed in Table 1, and the resulting weighted dimple profiles, from the use of these functions, is shown in <figref idref="DRAWINGS">FIGS. 1-23</figref> and Table 2. The cross-sections of half of a dimple profile are depicted in each figure, showing the dimple profile from the dimple center to the outer edge or golf ball surface. Specifically, three dashed lines are shown depicting the ball surface, chord plane and a base profile. For the examples, one base profile is used. All examples started with a spherical base profile having a dimple diameter of 0.2 inches, edge angle of 14°, and a chord depth, or maximum dimple depth at the center of the dimple measured from the chord plane of 0.0063 inches. This selected base profile is then weighted with a weighting function, for example by multiplying with a function chosen from Table 1, to achieve a weighted dimple profile, the solid line, as depicted in <figref idref="DRAWINGS">FIGS. 1-23</figref>. As is readily apparent from <figref idref="DRAWINGS">FIGS. 1-23</figref> and shown in Table 3, the base dimple profile and the weighted dimple profile have the same dimple diameters; however, they have one or more distinctly different dimple features; namely a different edge angle, volume, chord depth or dimple profile shape. Thus, the resulting claimed weighted dimple profile is uniquely different from the initial base dimple profile.

0067Turning to <figref idref="DRAWINGS">FIG. 24</figref>, ball <b>10</b> is shown as a finished ball including layers of paint and clear coat which creates a varied curvature at the demarcation between ball surface <b>12</b> and dimple wall <b>14</b>. This curvature makes the location of the dimple edge indistinct. In this case, the edge angle Φ is defined to be the angle between tangents T1 and T2. T2 is the tangent to the dimple wall <b>14</b> at the inflection point I. T1 is the tangent to the ball periphery surface <b>12</b> at point X which is the intersection of T2 and periphery <b>12</b>.

0068As shown in Table 2, the final weighted dimple profile has a chord depth, an equivalent spherical edge angle, an edge angle, and weighted volume ratio. As will be understood to one of ordinary skill in the art, the equivalent spherical edge angle is the edge angle of a spherical dimple with an equivalent chord volume and diameter. For example, for the weighted dimple profile in <figref idref="DRAWINGS">FIG. 1</figref> a spherical dimple with an equivalent chord volume and the same diameter would have an equivalent spherical edge angle of 21.08° while the edge angle as defined in <figref idref="DRAWINGS">FIG. 24</figref> is about 20.95°. The equivalent spherical edge angle of the weighted dimple profile is preferably within a range having a lower limit of about 10° or 11° or 12° and an upper limit of 20° or 21° or 22°. Additionally, as is understood in the art, the weighted volume ratio is the ratio of the volume of the weighted dimple profile to the base dimple profile. The volumes of both the weighted dimple profile and the base dimple profile are calculated using the chord plane, and thus, are considered to be chord volumes. Referring to <figref idref="DRAWINGS">FIGS. 25<i>a</i>-25<i>d</i></figref>, the chord volume <b>103</b> is shown. <figref idref="DRAWINGS">FIGS. 25<i>a</i>-25<i>c </i></figref>depict the ball surface <b>100</b>, the dimple surface <b>101</b> and the chord plane <b>102</b>. <figref idref="DRAWINGS">FIG. 25<i>d </i></figref>shows the enclosed volume of the dimple as the chord volume <b>103</b> bounded by the dimple surface <b>101</b> and the dimple chord plane <b>102</b>. For example, as listed in Table 2 the weighted volume ratio for the weighted dimple profile in <figref idref="DRAWINGS">FIG. 1</figref> is 2.00 using volumes calculated from the chord plane. Specifically, the weighted dimple profile shown in <figref idref="DRAWINGS">FIG. 1</figref> has a volume that is two times the volume of the base dimple profile shown in <figref idref="DRAWINGS">FIG. 1</figref> from the chord plane. The weighted dimple volume ratio of the weighted dimple profile to the base dimple profile is preferably within a range having a lower limit of 0.2 or 0.4 or 0.6 and an upper limit of 2 or 3 or 4.

0069It will be appreciated when viewing <figref idref="DRAWINGS">FIG. 1</figref> that the base dimple profile and the weighted dimple profile have the same dimple diameter; however, the chord depth, edge angle and volume of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 2.00.

0070As shown in <figref idref="DRAWINGS">FIGS. 2-9, 13 and 16</figref>, the base dimple profile and the weighted dimple profile have the same dimple diameter and the same chord depth; however, the volume and the edge angle of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.17 to about 1.70.

0071<figref idref="DRAWINGS">FIGS. 10-12, 14 and 17</figref> show that the base dimple profile and the weighted dimple profile have the same dimple diameter and the same edge angle; however, the volume and the chord depth of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.47 to about 1.77.

0072Referring now to <figref idref="DRAWINGS">FIGS. 15, 18 and 19</figref> it is apparent that the base dimple profile and the weighted dimple profile have the same dimple diameter, chord depth and edge angle; however, the volume of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.15 to about 1.21.

0073As shown in <figref idref="DRAWINGS">FIG. 20</figref>, the base dimple profile and the weighted dimple profile have the same edge angle and volume; however, the chord depth of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.00, meaning the volume of the base dimple profile and the weighted dimple profile are substantially the same.

0074<figref idref="DRAWINGS">FIG. 21</figref> shows that the base dimple profile and the weighted dimple profile have the same dimple diameter and volume; however, the edge angle and chord depth of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.00, meaning the volume of the base dimple profile and the weighted dimple profile are substantially the same.

0075When viewing <figref idref="DRAWINGS">FIG. 22</figref> it is apparent that the base dimple profile and the weighted dimple profile have the same dimple diameter, volume and chord depth; however, the edge angle of the base dimple profile and the weighted dimple profile are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.00, meaning the volume of the base dimple profile and the weighted dimple profile are substantially the same.

0076Finally, with regard to <figref idref="DRAWINGS">FIG. 23</figref> it is apparent that the base dimple profile and the weighted dimple profile have the same dimple diameter, edge angle, volume and chord depth. It will be appreciated from the figure that the dimple profile shape of the base dimple profile and the weighted dimple profile are different, such that the cross-sectional shape of the dimple profiles are different. It will also be appreciated from Table 2, that the weighted volume ratio is about 1.00, meaning the volume of the base dimple profile and the weighted dimple profile are substantially the same.

0077Referring now to <figref idref="DRAWINGS">FIG. 26</figref>, the preferred plan shape area and total dimple volume are shown. The dimple plan shapes are preferably circular. The plan shape area is based on a planar view of the dimple plan shape, such that the viewing plane is normal to an axis connecting the center of the ball to the point of the calculated surface depth. The dimple volume is the total volume encompassed by the dimple shape and the surface of the golf ball. The plan shape area and total dimple volume preferably fall within range <b>1</b> in <figref idref="DRAWINGS">FIG. 26</figref>. More preferably, the dimple shape area and total dimple volume fall within range <b>2</b> shown in FIG. <b>26</b>. More specifically, preferably the dimple plan shape area is from about 0.0025 in²to about 0.045 in². More preferably, the dimple plan shape area is from about 0.0065 in²to about 0.036 in². Preferably, the dimple surface volume is from about 0.1×10⁻⁵in³to about 5.0×10⁻⁴in³. More preferably, the dimple surface volume is from about 0.3×10⁻⁴in³to about 3.3×10⁻⁴in³.

0078Dimple profiles of the present invention are defined by a spherical base profile, shown in <figref idref="DRAWINGS">FIG. 27</figref>, to which a weighting function is applied as a multiplier as discussed above. It will be appreciated that multiple weighting functions can be used. Regardless, the resulting dimple profile may remain smooth and continuous from the center of the dimple to the dimple edge, from about x=0 to about x=d/2. It will be appreciated that it will not necessarily be smooth across the entire dimple profile from −d/2 to d/2 because a discontinuity may exist at x=0.

0079In one embodiment, the base profile is modified using a pure weighted method. This method produces a weighted function, ƒ(x), in accordance with equation 1, as follows: <br />ƒ(<i>x</i>)=<i>g</i>(<i>x</i>)*<i>w</i>(<i>x</i>)  (1)

0080where,

0081g(x) is the Base Profile Function and

0082w(x) is the Weighting function

0000The pure weighting method means the resulting weighted function is purely a percentage of the original base profile function as defined by the weighting function.

0083In another embodiment, the base profile is modified using a profile relative weighted method. This method produces a weighted function, ƒ(x), in accordance with equation 2, as follows: <br />ƒ(<i>x</i>)=<i>g</i>(<i>x</i>)*(1+<i>w</i>(<i>x</i>))  (2)

0084where again,

0085g(x) is the Base Profile Function and

0086w(x) is the Weighting function

0000The profile relative method applies the given weighting function relative to the existing base profile function such that the weighted value is added to the existing base curve to obtain the resulting weighted function.

0087The weighting function w(x) is always continuous and applied from the dimple center at x=0 to the dimple perimeter at x=d/2 where d is the dimple diameter. Further, g(x) and f(x) are equal at x=d/2, the dimple chord plane.

0088It will be appreciated that both the profile relative method and the pure weighting method hold to the construct that the weighted function results from the multiplication of a base profile function and a weighting function. Further, the domain of the function w(x) is such that 0≤w(x)≤1 while the calculated weighted function range differs between the profile relative and pure weighting methods.

0089An example is shown in <figref idref="DRAWINGS">FIGS. 28<i>a</i>-<i>c</i></figref>. The spherical base function of <figref idref="DRAWINGS">FIG. 27</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 28</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=<i>x </i><br /> The weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. Cross-sectional views of the resulting dimple profile are shown in <figref idref="DRAWINGS">FIGS. 28<i>b </i>and 28<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 28<i>b </i></figref>is the resulting cross-section when using the profile relative method, while <figref idref="DRAWINGS">FIG. 28<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0090Another example is shown in <figref idref="DRAWINGS">FIGS. 29<i>a</i>-29<i>c</i></figref>. The spherical base function of <figref idref="DRAWINGS">FIG. 27</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 29</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=−<i>x</i>⁴<i>+x</i>³+2<i>x </i>

0091The weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. Cross-sectional views of the resulting dimple profile are shown in <figref idref="DRAWINGS">FIGS. 29<i>b </i>and 29<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 29<i>b </i></figref>is the resulting cross-section when using the profile relative method, and <figref idref="DRAWINGS">FIG. 29<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0092Dimple profiles of the present invention are defined by a catenary base profile to which a weighting function is applied as a multiplier as discussed above. An example of a catenary base profile is shown in <figref idref="DRAWINGS">FIG. 30</figref>, and described in U.S. Pat. No. 7,641,572, incorporated herein by reference in its entirety. For purposes of the present disclosure, a catenary base profile is defined by the following function:

0093<maths id="MATH-US-00003" num="00003"><math overflow="scroll"><mrow><mi>y</mi><mo>=</mo><mfrac><mrow><msub><mi>d</mi><mi>c</mi></msub><mo>⁡</mo><mrow><mo>(</mo><mrow><mrow><mi>cosh</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>sf</mi><mo>*</mo><mi>x</mi></mrow><mo>)</mo></mrow></mrow><mo>-</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mi>cosh</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>sf</mi><mo>*</mo><mfrac><mi>D</mi><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></math></maths><br /> where, for the above formula, <br /> y is the vertical direction coordinate away from the center of the ball with 0 at the center of the dimple <br /> x=the horizontal (radial) direction coordinate from the dimple apex to the dimple surface with 0 at the center of the dimple; <br /> sf=the shape factor; <br /> d_c=the chordal depth of the dimple, in inches; and <br /> D=the diameter of the dimple, in inches.

0094For the examples in <figref idref="DRAWINGS">FIGS. 31<i>a</i>-32<i>c</i></figref>, one base catenary profile is used. All examples started with a catenary base profile having a dimple diameter of 0.2 inches, a chord depth of 0.0035 inches and a shape factor of 100. It will be appreciated that a base profile may be used having a chord depth, or maximum dimple depth at the center of the dimple measured from the chord plane of 0.0015 to 0.0070 inches, and a shape factor of 30 to 300. The selected base profile is then weighted with a weighting function, for example by multiplying with a function chosen from Table 1, to achieve a weighted dimple profile.

0095It will be appreciated that multiple weighting functions can be used. Regardless, the resulting dimple profile may remain smooth and continuous from the center of the dimple to the dimple edge, from about x=0 to about x=d/2. It will be appreciated that it will not necessarily be smooth across the entire dimple profile from −d/2 to d/2 because a discontinuity may exist at x=0.

0096As discussed above, the catenary base profile may be modified using either a pure weighted method or a profile relative method. It will be appreciated that both the profile relative method and the pure weighting method hold to the construct that the weighted function results from the multiplication of a base profile function and a weighting function. Further, the domain of the function w(x) is such that 0≤w(x)≤1 while the calculated weighted function range differs between the profile relative and pure weighting methods.

0097It will be appreciated that similar to Table 3 above, the catenary base dimple profile and the resulting weighted dimple profile may have the same or different properties of diameter, shape factor, volume and chord depth.

0098An example is shown in <figref idref="DRAWINGS">FIGS. 31<i>a</i>-<i>c</i></figref>. The catenary base function of <figref idref="DRAWINGS">FIG. 30</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 31</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=<i>x </i><br /> The weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. A cross-sectional view of the resulting dimple is shown in <figref idref="DRAWINGS">FIGS. 31<i>b </i>and 31<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 31<i>b </i></figref>is the resulting cross-section when using the profile relative method, while <figref idref="DRAWINGS">FIG. 31<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0099Another example is shown in <figref idref="DRAWINGS">FIGS. 32<i>a</i>-32<i>c</i></figref>. The catenary base function of <figref idref="DRAWINGS">FIG. 30</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 32</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=−<i>x</i>⁴<i>+x</i>³+2<i>x </i>

0100This weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. Cross-sectional views of the resulting dimple are shown in <figref idref="DRAWINGS">FIGS. 32<i>b </i>and 32<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 32<i>b </i></figref>is the resulting cross-section when using the profile relative method, and <figref idref="DRAWINGS">FIG. 32<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0101Dimple profiles of the present invention are defined by a conical base profile to which a weighting function is applied as a multiplier as discussed above. An example of a conical base profile is shown in <figref idref="DRAWINGS">FIG. 33</figref>. The conical base profile may have a preferred edge angle of about 10° to about 13.5°, and a preferred chord depth of about 0.0063 to about 0.0105 inches. In another embodiment, the base profile may be conical with a bottom spherical cap as described in U.S. Pat. Nos. 8,137,217 and 8,632,426 and U.S. application Ser. No. 14/981,383 filed Dec. 28, 2015, incorporated herein by reference in their entirety. In this case, the base dimple profile comprises a top conical sidewall, a bottom spherical cap, and a defined point of tangency at an intersection between the top conical sidewall and bottom spherical cap, wherein a difference between a slope of the conical sidewall and a slope of the spherical cap is less than about 2°. The dimple has a shape defined by at least a saucer ratio and edge angle. The saucer ratio is defined as a ratio of dimple diameter to saucer diameter or spherical cap diameter, and the value of said ratio is between about 0.05 and about 0.75.

0102For the examples in <figref idref="DRAWINGS">FIGS. 34<i>a</i>-35<i>c</i></figref>, one base conical profile is used. All examples started with a conical base profile having a dimple diameter of 0.2 inches, edge angle of 10.4°, and a chord depth, or maximum dimple depth at the center of the dimple measured from the chord plane of 0.0049 inches. This selected base profile is then weighted with a weighting function, for example by multiplying with a function chosen from Table 1, to achieve a weighted dimple profile.

0103It will be appreciated that multiple weighting functions can be used. Regardless, the resulting dimple profile may remain smooth and continuous from the center of the dimple to the dimple edge, from about x=0 to about x=d/2. It will be appreciated that it will not necessarily be smooth across the entire dimple profile from −d/2 to d/2 because a discontinuity may exist at x=0.

0104As discussed above, the conical base profile may be modified using either a pure weighted method or a profile relative method. It will be appreciated that both the profile relative method and the pure weighting method hold to the construct that the weighted function results from the multiplication of a base profile function and a weighting function. Further, the domain of the function w(x) is such that 0≤w(x)≤1 while the calculated weighted function range differs between the profile relative and pure weighting methods.

0105It will be appreciated that similar to Table 3 above, the catenary base dimple profile and the resulting weighted dimple profile may have the same or different properties of diameter, edge angle, volume and chord depth.

0106An example is shown in <figref idref="DRAWINGS">FIGS. 34<i>a</i>-<i>c</i></figref>. The conical base function of <figref idref="DRAWINGS">FIG. 33</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 34</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=<i>x </i><br /> The weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. A cross-sectional view of the resulting dimple is shown in <figref idref="DRAWINGS">FIGS. 34<i>b </i>and 34<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 34<i>b </i></figref>is the resulting cross-section when using the profile relative method, while <figref idref="DRAWINGS">FIG. 34<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0107Another example is shown in <figref idref="DRAWINGS">FIGS. 35<i>a</i>-35<i>c</i></figref>. The conical base function of <figref idref="DRAWINGS">FIG. 33</figref> is modified using the weighting function shown in <figref idref="DRAWINGS">FIG. 35</figref><i>a: </i><br /><i>w</i>(<i>x</i>)=−<i>x</i>⁴<i>+x</i>³+2<i>x </i><br /> The weighting function is continuous from the dimple center to the dimple perimeter and the weighting is applied as such thereby creating the weighted function representing a half dimple profile that is revolved about an axis through the dimple center to create the dimple surface. Cross-sectional views of the resulting dimple are shown in <figref idref="DRAWINGS">FIGS. 35<i>b </i>and 35<i>c </i></figref>using the two different weighting methods. <figref idref="DRAWINGS">FIG. 35<i>b </i></figref>is the resulting cross-section when using the profile relative method, and <figref idref="DRAWINGS">FIG. 35<i>c </i></figref>is the resulting cross-section when using the pure weighted method.

0108In another embodiment of the present invention, dimples on a golf ball have a cross section which is defined by two or more of a spherical base curve, a conical base curve or a catenary base curve that have been modified by a continuous weighting function or filter as described above. The resulting golf ball has at least two dimples modified with a continuous weighting function that have different base profiles. The dimple base profiles may be modified with any continuous weighting function, for example such as those identified above in Table 2. It will be appreciated that more than two dimples may be modified with a continuous weighting function, and that more than two different base profiles may be used in the dimples modified with a continuous weighting function. Additionally, it will be understood that the dimples may be modified using a pure weighting method or a profile relative method as described above.

0109In one embodiment, every dimple will have modified cross-sections defined by weighting functions. In another embodiment, the number of dimples using the first weighted base profile is equal to the number of dimples using the second weighted base profile. In another embodiment, the number of dimples using a first weighted base profile is not equal to the number of dimples using the second weighted base profile. In an additional embodiment of the invention, the golf ball also may include dimples that have cross-sections that have not been modified by a weighting function.

0110The following three examples shown in <figref idref="DRAWINGS">FIGS. 36-38</figref>, illustrate a section <b>200</b>, <b>204</b>, <b>210</b> of a golf ball made with a hexagonal dipyramid pattern such that the section represents 1/12 of the golf ball. The pattern in the examples has 338 dimples, resulting in each section having of 28 and 1/16 dimples. As is known in the art, the sections <b>200</b>, <b>204</b>, <b>210</b> are tiled on the golf ball to form a dimple pattern. Although sections <b>200</b>, <b>204</b>, <b>210</b> made with a hexagonal dipyramid pattern are illustrated, it will be appreciated that any suitable pattern may be used.

0111In the example shown in <figref idref="DRAWINGS">FIG. 36</figref> and Table 4, the section <b>200</b> is made entirely of dimples <b>202</b> that have cross-sectional profiles that have been modified by weighting functions. The labels A and B represent the type of cross-sectional profile of the dimple <b>202</b>. In this example, dimples <b>202</b> labeled A have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a spherical base profile function g(x) and at least one weighting function w(x). The dimples <b>202</b> labeled B have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x). Both dimples types A, B are created using the pure weighting method described above.

0112<tables id="TABLE-US-00004" num="00004"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="35pt" align="left" /><colspec colname="2" colwidth="56pt" align="left" /><colspec colname="3" colwidth="42pt" align="left" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="center" /><thead><row><entry /><entry namest="offset" nameend="5" rowsep="1">TABLE 4</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row><row><entry /><entry /><entry /><entry /><entry>Number </entry><entry>Number </entry></row><row><entry /><entry /><entry /><entry /><entry>of </entry><entry>of</entry></row><row><entry /><entry /><entry>Dimple</entry><entry /><entry>Dimples</entry><entry>dimples </entry></row><row><entry /><entry>Dimple</entry><entry>Cross-</entry><entry>Weighting</entry><entry>in the </entry><entry>on the</entry></row><row><entry /><entry>Label</entry><entry>Section</entry><entry>Method</entry><entry>Segment</entry><entry>Ball</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="35pt" align="center" /><colspec colname="2" colwidth="56pt" align="center" /><colspec colname="3" colwidth="42pt" align="center" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="center" /><tbody valign="top"><row><entry /><entry>A</entry><entry>Weighted</entry><entry>Pure</entry><entry>15 1/6</entry><entry>182</entry></row><row><entry /><entry /><entry>Spherical Base</entry><entry>Weighting</entry><entry /><entry /></row><row><entry /><entry>B</entry><entry>Weighted</entry><entry>Pure</entry><entry>13</entry><entry>156</entry></row><row><entry /><entry /><entry>Catenary Base</entry><entry>Weighting</entry><entry /><entry /></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0113In the example shown in <figref idref="DRAWINGS">FIG. 37</figref> and Table 5, the section <b>204</b> is made of dimples <b>206</b> that have cross-sectional profiles that have been modified by weighting functions. The labels A and B represent the type of cross-sectional profile of the dimple <b>206</b>. In this example, dimples <b>206</b> labeled A have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a conical base profile function g(x) and at least one weighting function w(x). The dimples <b>206</b> labeled B have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x). Both dimple types A, B are created using the profile relative weighting method. Dimples <b>208</b> that are not labeled in the figure are spherical dimples that are not modified by any kind of weighting function.

0114<tables id="TABLE-US-00005" num="00005"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="28pt" align="center" /><colspec colname="2" colwidth="49pt" align="center" /><colspec colname="3" colwidth="56pt" align="center" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="center" /><thead><row><entry /><entry namest="offset" nameend="5" rowsep="1">TABLE 5</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row><row><entry /><entry /><entry /><entry /><entry>Number </entry><entry>Number </entry></row><row><entry /><entry /><entry /><entry /><entry>of </entry><entry>of</entry></row><row><entry /><entry /><entry>Dimple</entry><entry /><entry>Dimples</entry><entry>dimples </entry></row><row><entry /><entry>Dimple</entry><entry>Cross-</entry><entry>Weighting</entry><entry>in the </entry><entry>on the</entry></row><row><entry /><entry>Label</entry><entry>Section</entry><entry>Method</entry><entry>Segment</entry><entry>Ball</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="28pt" align="center" /><colspec colname="2" colwidth="49pt" align="center" /><colspec colname="3" colwidth="56pt" align="center" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="char" char="." /><tbody valign="top"><row><entry /><entry>A</entry><entry>Weighted</entry><entry>Profile</entry><entry>10</entry><entry>120</entry></row><row><entry /><entry /><entry>Conical Base</entry><entry>Relative</entry><entry /><entry /></row><row><entry /><entry>B</entry><entry>Weighted</entry><entry>Profile</entry><entry>10</entry><entry>120</entry></row><row><entry /><entry /><entry>Catenary Base</entry><entry>Relative</entry><entry /><entry /></row><row><entry /><entry>NONE</entry><entry>Spherical</entry><entry>NA</entry><entry>8 1/6</entry><entry>98</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0115In the example shown in <figref idref="DRAWINGS">FIG. 38</figref> and Table 6, the section <b>210</b> is made entirely of dimples <b>212</b> that have cross-sectional profiles that have been modified by weighting functions. The labels A, B and C represent the type of cross-sectional profile of the dimple <b>212</b>. In this example, dimples <b>212</b> labeled A have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a conical base profile function g(x) and at least one weighting function w(x). The dimples <b>212</b> labeled B have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a catenary base profile function g(x) and at least one weighting function w(x). The dimples <b>212</b> labeled C have a cross-sectional profile defined by a weighted function, where the weighted function is the multiplication of a spherical base profile function g(x) and at least one weighting function w(x). The dimples types A and C are created using a profile relative method and the dimple type B is created using the pure weighting method.

0116<tables id="TABLE-US-00006" num="00006"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="28pt" align="center" /><colspec colname="2" colwidth="49pt" align="center" /><colspec colname="3" colwidth="56pt" align="center" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="center" /><thead><row><entry /><entry namest="offset" nameend="5" rowsep="1">TABLE 6</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row><row><entry /><entry /><entry /><entry /><entry>Number </entry><entry>Number </entry></row><row><entry /><entry /><entry /><entry /><entry>of </entry><entry>of</entry></row><row><entry /><entry /><entry>Dimple</entry><entry /><entry>Dimples</entry><entry>dimples</entry></row><row><entry /><entry>Dimple</entry><entry>Cross-</entry><entry>Weighting</entry><entry>in the </entry><entry>on the</entry></row><row><entry /><entry>Label</entry><entry>Section</entry><entry>Method</entry><entry>Segment</entry><entry>Ball</entry></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /></row></tbody></tgroup><tgroup align="left" colsep="0" rowsep="0" cols="6"><colspec colname="offset" colwidth="14pt" align="left" /><colspec colname="1" colwidth="28pt" align="center" /><colspec colname="2" colwidth="49pt" align="center" /><colspec colname="3" colwidth="56pt" align="center" /><colspec colname="4" colwidth="28pt" align="center" /><colspec colname="5" colwidth="42pt" align="char" char="." /><tbody valign="top"><row><entry /><entry>A</entry><entry>Weighted</entry><entry>Profile</entry><entry>12 1/6</entry><entry>146</entry></row><row><entry /><entry /><entry>Conical Base</entry><entry>Relative</entry><entry /><entry /></row><row><entry /><entry>B</entry><entry>Weighted</entry><entry>Pure</entry><entry>10</entry><entry>120</entry></row><row><entry /><entry /><entry>Catenary Base</entry><entry>Weighting</entry><entry /><entry /></row><row><entry /><entry>C</entry><entry>Weighted</entry><entry>Profile</entry><entry>6</entry><entry>72</entry></row><row><entry /><entry /><entry>Spherical Base</entry><entry>Relative</entry><entry /><entry /></row><row><entry /><entry namest="offset" nameend="5" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>

0117It will be appreciated that the above are examples showing use of a particular base function with a particular weighting function with either the profile relative method or the pure weighting method. These weighting methods may be used with any of the equations discussed herein, or any other equation known to one of skill in the art.

0118The present invention is not limited by any particular dimple pattern. Examples of suitable dimple patterns include, but are not limited to, phyllotaxis-based patterns; polyhedron-based patterns; and patterns based on multiple copies of one or more irregular domain(s) as disclosed in U.S. Pat. No. 8,029,388, the entire disclosure of which is hereby incorporated herein by reference; and particularly dimple patterns suitable for packing dimples on seamless golf balls. Non-limiting examples of suitable dimple patterns are further disclosed in U.S. Pat. Nos. 7,927,234, 7,887,439, 7,503,856, 7,258,632, 7,179,178, 6,969,327, 6,702,696, 6,699,143, 6,533,684, 6,338,684, 5,842,937, 5,562,552, 5,575,477, 5,957,787, 5,249,804, 5,060,953, 4,960,283, and 4,925,193, and U.S. Patent Application Publication Nos. 2006/0025245, 2011/0021292, 2011/0165968, and 2011/0183778, the entire disclosures of which are hereby incorporated herein by reference. Non-limiting examples of seamless golf balls and methods of producing such are further disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.

0119In a particular embodiment, the dimple pattern provides for overall dimple coverage of 60% or greater, or 65% or greater, or 75% or greater, or 80% or greater, or 85% or greater, or 90% or greater.

0120Golf balls of the present invention typically have a dimple count within a limit having a lower limit of 250 and an upper limit of 350 or 400 or 450 or 500. In a particular embodiment, the dimple count is 252 or 272 or 302 or 312 or 320 or 328 or 332 or 336 or 340 or 352 or 360 or 362 or 364 or 372 or 376 or 384 or 390 or 392 or 432.

0121Preferably, at least 30%, or at least 50%, or at least 60%, or at least 80%, or at least 90%, or at least 95% of the total number of dimples have a cross-sectional profile defined by the product of a base function and at least one weighting function, with the remaining dimples, if any, having a cross-sectional profile based on any known dimple profile shape including, but not limited to, parabolic curves, ellipses, spherical curves, saucer-shapes, sine curves, truncated cones, flattened trapezoids, and catenary curves. Among the dimples having a cross-sectional profile defined by the present invention, the profile of one dimple may be the same as or different from the profile of another dimple. Similarly, among the remaining dimples, if any, having a known dimple profile shape, the profile of one dimple may be the same as or different from the profile of another dimple.

0122The diameter of the dimples is preferably within a range having a lower limit of 0.090 inches or 0.100 inches or 0.115 inches or 0.125 inches and an upper limit of 0.185 inches or 0.200 inches or 0.225 inches.

0123The chord depth of the dimples is preferably within a range having a lower limit of 0.002 inches or 0.003 inches or 0.004 inches or 0.006 inches and an upper limit of 0.008 inches or 0.010 inches or 0.012 inches or 0.014 inches or 0.016 inches.

0124The present invention is not limited by any particular golf ball construction or any particular composition for forming the golf ball layers. For example, functionally weighted curves of the present invention can be used to form dimple profiles on one-piece, two-piece (i.e., a core and a cover), multi-layer (i.e., a core of one or more layers and a cover of one or more layers), and wound golf balls, having a variety of core structures, intermediate layers, covers, and coatings.

0125When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used.

0126All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted.

0127While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains.